Reconstruction of Quadrics from Two Polarization Views

This paper addresses the problem of reconstructing texture-less objects of quadric like shape. It is known that a quadric can be uniquely recovered from its apparent contours in three views. But, in the case of only two views the reconstruction is a one parameter family of quadrics. Polarization imaging provides additional geometric information compared to simple intensity based imaging. The polarization image encodes the projection of the surface normals onto the image and therefore provides constraints on the surface geometry. In this paper it is proven that two polarization views of a quadric contain sufficient information for a complete determination of its shape. The proof itself is constructive leading to a closed-form solution for the quadric. Additionally, an indirect algorithm is presented which uses both polarization and apparent contours. By experiments it is shown that the presented algorithm produces accurate reconstruction results.